When I say ignoring I do not mean I have no idea what they are up to, I always know. When they need me I am still there. They know this therefore they are secure and able to occupy themselves while I do something else.
I tried being the helicopter parent who schedules every damn second of my kids days. It sucked! When my daughter was a newborn I would bundle my kids up and walk 3 blocks to the library once a week for toddler story time. Winter session. -30. I. Despised. It. I did it to appease my mother-in-law who is convinced that I do not do anything worthwhile with my kids. The only person who enjoyed the weekly trek was my baby girl, she was all wrapped up in a Sleepy Wrap under my over-sized winter coat and usually sleeping. My son? Well, I do not think he much cared for it, every week I was chasing my then 2 year old around a tiny room in the library trying to get him to just sit and listen to the story. Sounds like fun eh? I think he (and I) would have preferred our normal story time. It involves him grabbing a book, asking me to read it to him (several times) until he is bored and interested in something else.
My kids have an abundance of art supplies available at all times, they have lego, and cars, and barbies, and most importantly THEY HAVE IMAGINATIONS and freedom, they know they can get paint on the floor or all over themselves and nobody will get mad. I have some me time, I have the ability to clean the kitchen mess I did not make without interruption. I have happy, secure children who can play, really play and still know mommy is there. My kids have learned appropriate social skills such as sharing, and co-operation by simply playing together without interference or a grown up hovering, planning, or dragging them around every waking minute.